%%

c=1;
nu=1;

set(gca,'FontSize',18)
set(gca,'LineWidth',2)

f = (0:0.2:2).';
v = (-0.3:0.05:0.3);

f_matrix =f*ones(size(v));

v_matrix =ones(size(f))*v;

u_x = v_matrix;

u_y = 1/nu*v_matrix.*(f_matrix-c);


quiver(f_matrix,v_matrix,u_x,u_y,1,'LineWidth',2)
xlabel('u')
ylabel('w')
hold on
plot([0,2],[0,0],'g','LineWidth',2)
axis([0,2,-0.3,0.3])

hold off



% print -djpeg kdv_phase_portrait





for j = 1:9000;
    x(j+1) = x(j) + dt*y(j);
    y(j+1) = y(j) + dt*(c*x(j) - 3*x(j).*x(j));
    t(j+1) = t(j) + dt;
end

% we flow in along the incident manifold. 

for count = 3000:500:11000
subplot(2,1,1)
set(gca,'FontSize',18)
set(gca,'LineWidth',2)
quiver(f_matrix,v_matrix,u_x,u_y,1,'LineWidth',2)
xlabel('f')
ylabel('v')
hold on
plot(1,0,'o','MarkerFaceColor','r','MarkerSize',10)
plot(0,0,'o','MarkerFaceColor','g','MarkerSize',10)
M = [0,1,;1,-2];
[V,D] = eig(M);
r=0.1;
% plot_arrow(1,0,1+r*V(1,2),r*V(2,2),...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)
% plot_arrow(1,0,1-r*V(1,2),-r*V(2,2),...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)
% 
% plot_arrow(1+r*V(1,1),r*V(2,1),1,0,...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)
% plot_arrow(1-r*V(1,1),-r*V(2,1),1,0,...
%     'linewidth',2,'headwidth',0.25,'headheight',0.33)

plot(x(count),y(count),'d','MarkerFaceColor','k','MarkerSize',10)

axis([-0.2,1.5,-1,1])


plot(x,y,'c','LineWidth',2)
    
hold off

subplot(2,1,2)
set(gca,'FontSize',18)
set(gca,'LineWidth',2)
plot(t,x,'LineWidth',2)
% axis([0,15,-0.2,2])
xlabel('\zeta')
ylabel('f')
hold on
plot(t(count),x(count),'d','MarkerFaceColor','k','MarkerSize',10)
 gif_add_frame(gcf,'kdv_wave_solitary.gif',2);
hold off
end

figure

clear x y t
r=0.0001;
x(1) = 0.2;
y(1) = 0;
dt = 0.001;
t(1) = 0;

for j = 1:15000;
    x(j+1) = x(j) + dt*y(j);
    y(j+1) = y(j) + dt*(c*x(j) - 3*x(j).*x(j));
    t(j+1) = t(j) + dt;
end


delete kdv_wave_cn.gif
for count = 3000:500:11000
subplot(2,1,1)
set(gca,'FontSize',18)
set(gca,'LineWidth',2)
quiver(f_matrix,v_matrix,u_x,u_y,1,'LineWidth',2)
xlabel('f')
ylabel('v')
hold on
plot(1,0,'o','MarkerFaceColor','r','MarkerSize',10)
plot(0,0,'o','MarkerFaceColor','g','MarkerSize',10)
M = [0,1,;1,-2];
[V,D] = eig(M);
r=0.1;

plot(x(count),y(count),'d','MarkerFaceColor','k','MarkerSize',10)

axis([-0.2,1.5,-1,1])


plot(x(1:6000),y(1:6000),'c','LineWidth',2)
    
hold off

subplot(2,1,2)
set(gca,'FontSize',18)
set(gca,'LineWidth',2)
plot(t,x,'LineWidth',2)
% axis([0,15,-0.2,2])
xlabel('\zeta')
ylabel('f')
hold on
plot(t(count),x(count),'d','MarkerFaceColor','k','MarkerSize',10)
 gif_add_frame(gcf,'kdv_wave_cn.gif',2);
hold off
end